Newton's laws

1. Introduction

2. Force

3. Basic types of forces

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William is investigating the motion of an object as it slides to the right along a rough horizontal surface.

The following force diagram shows all the forces exerted on the object except for the normal force.

Which one of the following force diagrams shows the correct size and direction of the normal force $\vec{F}_{\text{N}}$ ?

Answer:

The normal force is correctly shown in diagram:

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Luyanda is investigating the motion of a crate as it slides down a rough wooden ramp.

The following free-body diagram shows all the forces exerted on the crate except for the normal force.

Which one of the following free-body diagrams shows the correct size and direction of the normal force $\vec{F}_{\text{N}}$ ?

Answer:

The normal force is correctly shown in diagram:

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An object is sliding along a rough horizontal surface.

As the object slides, it experiences the kinetic frictional force $(\vec{f}_{\text{k}})$ . Various properties of the object and the surface will affect this force, but some will not.

For each property below, decide whether it does or does not affect the magnitude of the kinetic frictional force experienced by the object.
Answer:
The magnitude of the kinetic frictional force is affected by:
- the contact surface area between the object and the surface:
- the distance travelled by the object:
- the material the object is made from:

The object is covered with a thin layer of smoother material. Will the magnitude of the kinetic frictional force increase, decrease, or remain the same?

Select a reason for your answer from the table of reasons given below. Assume that all other properties of the object and the horizontal surface remain the same.

A	The object and surface will be pushing into each other less and so the normal force on the object will decrease.
B	It will be easier for the object to slide because the coefficient of friction between the object and the surface will decrease.
C	The object and surface will be pushing into each other more and so the normal force on the object will increase.
D	It will be harder for the object to slide because the coefficient of friction between the object and the surface will increase.

Answer:

If the object is covered with a thin layer of smoother material, the magnitude of the kinetic frictional force will .

This is because of Reason .

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A box is sliding along a rough horizontal surface.

As the box slides, it experiences the kinetic frictional force $(\vec{f}_{\text{k}})$ . Various properties of the box and the surface will affect this force, but some will not.

For each property below, decide whether it does or does not affect the magnitude of the kinetic frictional force experienced by the box.
Answer:
The magnitude of the kinetic frictional force is affected by:
- the material the box is made from:
- the speed of box:
- the material the surface is made from:

The surface is covered with a thin layer of smoother material. Will the magnitude of the kinetic frictional force increase, decrease, or remain the same?

Select a reason for your answer from the table of reasons given below. Assume that all other properties of the box and the horizontal surface remain the same.

A	The box and surface will be pushing into each other less and so the normal force on the box will decrease.
B	It will be harder for the box to slide because the coefficient of friction between the box and the surface will increase.
C	The box and surface will be pushing into each other more and so the normal force on the box will increase.
D	It will be easier for the box to slide because the coefficient of friction between the box and the surface will decrease.

Answer:

If the surface is covered with a thin layer of smoother material, the magnitude of the kinetic frictional force will .

This is because of Reason .

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Define the coefficient of kinetic friction using the dropdown menus below.

Answer:

The coefficient of kinetic friction $(\mu_{\text{k}})$ is defined as the the and experienced by an object in contact with a surface.

It is which means it . It depends on .

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Define the coefficient of static friction using the dropdown menus below.

Answer:

The coefficient of static friction $(\mu_{\text{s}})$ is defined as the the and experienced by an object in contact with a surface.

It is which means it . It depends on .

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Iminathi is investigating the motion of a box as it slides up a rough wooden ramp.

The following free-body diagram shows all the forces exerted on the box.

Iminathi now increases $\alpha$ , the angle of the ramp.

Will the magnitude of the normal force experienced by the box increase, decrease, or remain the same? Give a reason for your answer.

Answer:

The magnitude of the normal force will .

This is because increasing the angle of the ramp will the magnitude of the normal force.

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Richard is investigating the motion of a box as it slides down a rough wooden ramp.

The following force diagram shows all the forces exerted on the box.

Richard now increases $\alpha$ , the angle of the ramp.

Will the magnitude of the normal force experienced by the box increase, decrease, or remain the same? Give a reason for your answer.

Answer:

The magnitude of the normal force will .

This is because increasing the angle of the ramp will the magnitude of the normal force.

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The relationship $f_{\text{k}} = \mu_{\text{k}} F_{\text{N}}$ is an important equation in mechanics.

What does the symbol $f_{\text{k}}$ stand for?

Answer:
The symbol $f_{\text{k}}$ stands for the .
What is the SI unit used to measure $F_{\text{N}}$ ?

Answer:
The SI unit used to measure $F_{\text{N}}$ is .

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The relationship $f_{\text{s}}^{\text{max}} = \mu_{\text{s}} F_{\text{N}}$ is a useful equation in mechanics.

What does the symbol $F_{\text{N}}$ represent?

Answer:
The symbol $F_{\text{N}}$ represents the .
What is the SI unit in which we measure $\mu_{\text{s}}$ ?

Answer:
The SI unit in which we measure $\mu_{\text{s}}$ is .

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Nnenna is investigating the motion of a crate as it slides to the left along a rough horizontal surface.

The following force diagram shows all the forces exerted on the crate.

Nnenna now pushes the crate perpendicularly into the surface.

Will the magnitude of the normal force increase, decrease, or remain the same? Give a reason for your answer.

Answer:

The magnitude of the normal force will .

This is because pushing the crate perpendicularly into the surface will the magnitude of the force the crate exerts perpendicularly into the surface.

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Louise is investigating the motion of a box as it slides to the left along a rough horizontal surface.

The following free-body diagram shows all the forces exerted on the box.

Louise now pulls the box to the left parallel to the surface.

Will the magnitude of the normal force increase, decrease, or remain the same? Give a reason for your answer.

Answer:

The magnitude of the normal force will .

This is because pulling the box parallel to the surface will the magnitude of the force the box exerts perpendicularly into the surface.

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A box is sliding down a rough slope.

As the box slides, it experiences the kinetic frictional force $(\vec{f}_{\text{k}})$ . Various properties of the box and the slope will affect this force, but some will not.

For each property below, decide whether it does or does not affect the magnitude of the kinetic frictional force experienced by the box.
Answer:
The magnitude of the kinetic frictional force is affected by:
- the angle of inclination of the slope:
- the distance travelled by the box:
- the material the box is made from:

The box is covered with a thin layer of rougher material. Will the magnitude of the kinetic frictional force increase, decrease, or remain the same?

Select a reason for your answer from the table of reasons given below. Assume that all other properties of the box and the slope remain the same.

A	The box and the slope will be pushing into each other less and so the normal force on the box will decrease.
B	The box and the slope will be pushing into each other more and so the normal force on the box will increase.
C	It will be easier for the box to slide because the coefficient of friction between the box and the slope will decrease.
D	It will be harder for the box to slide because the coefficient of friction between the box and the slope will increase.

Answer:

If the box is covered with a thin layer of rougher material, the magnitude of the kinetic frictional force would .

This is because of Reason .

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A box is sliding down a rough slope.

As the box slides, it experiences the kinetic frictional force $(\vec{f}_{\text{k}})$ . Various properties of the box and the slope will affect this force, but some will not.

For each property below, decide whether it does or does not affect the magnitude of the kinetic frictional force experienced by the box.
Answer:
The magnitude of the kinetic frictional force is affected by:
- the material the slope is made from:
- the material the box is made from:
- the mass of the box:

The box was replaced with a box of smaller mass. Will the magnitude of the kinetic frictional force increase, decrease, or remain the same?

Select a reason for your answer from the table of reasons given below. Assume that all other properties of the box and the slope remain the same.

A	The box and the slope will be pushing into each other less and so the normal force on the box will decrease.
B	It will be easier for the box to slide because the coefficient of friction between the box and the slope will decrease.
C	It will be harder for the box to slide because the coefficient of friction between the box and the slope will increase.
D	The box and the slope will be pushing into each other more and so the normal force on the box will increase.

Answer:

If the box was replaced with a box of smaller mass, the magnitude of the kinetic frictional force would .

This is because of Reason .

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Objects can experience different forms of the frictional force: static friction, maximum static friction, and kinetic friction.

In the question below there is a list of four facts about each of these forces. Each list is missing two pieces of information. Complete the lists by selecting the correct choices.

Answer:

Static friction $(\vec{f}_{\text{s}})$

experienced by a object
does not have a formula
depend on the roughness of the surfaces in contact
does depend on other forces parallel to the surface

Maximum static friction $({\vec{f}_{\text{s}}}^{\text{max}})$

experienced by a object
does have a formula
depend on the roughness of the surfaces in contact
does not depend on other forces parallel to the surface

Kinetic friction $(\vec{f}_{\text{k}})$

experienced by a object
does have a formula
depend on the roughness of the surfaces in contact
does not depend on other forces parallel to the surface

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Objects can experience different forms of the frictional force: static friction, maximum static friction, and kinetic friction.

In the question below there is a list of four facts about each of these forces. Each list is missing two pieces of information. Complete the lists by selecting the correct choices.

Answer:

Static friction $(\vec{f}_{\text{s}})$

experienced by a stationary object
does not have a formula
depend on the roughness of the surfaces in contact
depend on other forces parallel to the surface

Maximum static friction $({\vec{f}_{\text{s}}}^{\text{max}})$

experienced by a stationary object
does have a formula
depend on the roughness of the surfaces in contact
depend on other forces parallel to the surface

Kinetic friction $(\vec{f}_{\text{k}})$

experienced by a moving object
does have a formula
depend on the roughness of the surfaces in contact
depend on other forces parallel to the surface

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3. Newton's laws

5. Force and free-body diagrams

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Define a free-body diagram using the dropdown menus below.

Answer:

A free-body diagram shows the of all forces exerted on an object using to represent the force vectors. The object is represented by and all force vectors have their tails at the and point .

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Define a force diagram using the dropdown menus below.

Answer:

A force diagram shows the of all forces exerted on an object using to represent the force vectors. The object is represented by and all force vectors have their tails at the and point .

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A number of different forces are acting on a suitcase. Chiamaka draws the following diagram to show all these forces.

Did Chiamaka draw a free-body diagram or a force diagram?

Give a reason for your answer from the table below.

A	the object is represented by an outline of the actual shape of the object with each force acting on the object drawn as an arrow pointing away from the point on the object at which the force acts
B	the object is represented by a dot with each force acting on the object drawn as an arrow pointing away from the dot

Answer:

Chiamaka drew a diagram.

We know this because .

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A number of different forces are acting on a box. Talatu draws the following diagram to show all these forces.

Did Talatu draw a free-body diagram or a force diagram?

Give a reason for your answer from the table below.

A	the object is represented by a dot with each force acting on the object drawn as an arrow pointing away from the dot
B	the object is represented by an outline of the actual shape of the object with each force acting on the object drawn as an arrow pointing away from the point on the object at which the force acts

Answer:

Talatu drew a diagram.

We know this because .

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A block of mass $m_{1}$ is connected to another block of mass $m_{2}$ by a light inextensible string. This system of blocks is then suspended from the ceiling by the top block, using the same type of string.

Draw labelled free-body diagrams indicating all the forces acting on each block.

Now compare your diagrams to the two diagrams given below and answer the questions that follow.

Diagram A

Diagram B
1. Which diagram is the free-body diagram for the bottom block?
2. Which force does Force $\vec{Q}$ represent?
Answer:
1. Diagram is the free-body diagram for the bottom block.
2. Force $\vec{Q}$ represents the force acting on the block.

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A block of mass $m_{1}$ is connected to another block of mass $m_{2}$ by a light inextensible rope. This system of blocks is then suspended from the ceiling by the top block, using the same type of rope.

Draw labelled free-body diagrams indicating all the forces acting on each block.

Now compare your diagrams to the two diagrams given below and answer the questions that follow.

Diagram A

Diagram B
1. Which diagram is the free-body diagram for the top block?
2. Which force does Force $\vec{Y}$ represent?
Answer:
1. Diagram is the free-body diagram for the top block.
2. Force $\vec{Y}$ represents the force acting on the block.

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Block $\text{1}$ is connected to Block $\text{2}$ by a light inextensible rope. The same type of rope is attached to Block $\text{2}$ , run over a light frictionless pulley, and connected to a motor.

The motor pulls the system up a smooth plane inclined at an angle $\alpha$ to the horizontal. The motor applies a constant force which causes the system to accelerate. The force applied by the motor is parallel to the plane as shown in the diagram below. Ignore all forms of friction.

Draw labelled free-body diagrams indicating all the forces acting on the both blocks.

How many forces should there be in these diagrams?Remember that a free-body diagram should contain actual forces, not components of forces.

Answer:

There is/are force(s) in the free-body diagram for the bottom block.
There is/are force(s) in the free-body diagram for the top block.

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type(string)

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type(string)

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Box $\text{1}$ is connected to Box $\text{2}$ by a light inextensible cable. The same type of cable is attached to Box $\text{2}$ , run over a light frictionless pulley, and connected to a motor.

Draw labelled free-body diagrams representing all the forces acting on the both boxes.

How many forces should there be in these diagrams?Remember that a free-body diagram should contain actual forces, not components of forces.

Answer:

There is/are force(s) in the free-body diagram for the bottom box.
There is/are force(s) in the free-body diagram for the top box.

one-of

type(string)

one-of

type(string)

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Box 1 is connected to Box 2 by a light inextensible rope. The system is pulled up a smooth slope inclined at $\alpha$ to the horizontal, by means of a constant force parallel to the slope as shown in the diagram below. All forms of friction can be ignored.

Draw a labelled free-body diagram showing all the forces acting on Box 1 as it moves up the slope.

The free-body diagram given below contains a mistake. There is a problem with one of the forces.

Compare your free-body diagram to the given diagram to work out which force is the problem and what the mistake is.

Possible mistakes
1	The force is missing.
2	The force has the wrong direction.
3	The force should not be there.

Answer:

The force with the problem is the force.

The problem is .

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Box 1 is connected to Box 2 by a light inextensible string. The system is pulled up a rough plane inclined at $\alpha$ to the horizontal, by means of a constant force parallel to the plane as shown in the diagram below. The magnitude of the kinetic frictional force between the surface and Box $\text{1}$ is $f_{\text{k}, 1}$ .

Draw a labelled free-body diagram indicating all the forces acting on Box 1 as it moves up the plane.

The free-body diagram given below contains a mistake. There is a problem with one of the forces.

Compare your free-body diagram to the given diagram to work out which force is the problem and what the mistake is.

Possible mistakes
1	The force is missing.
2	The force has the wrong direction.
3	The force should not be there.

Answer:

The force with the problem is the force.

The problem is .

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A system of two crates is pulled up a smooth ramp.

The string joining the two crates is inextensible (it can't be stretched) and it is pulled tight.

Xolile draws a diagram to show all the forces acting on one of the crates.

This is the diagram that she draws:

Which one of the options below best describes the diagram that Xolile drew?

A	A free-body diagram for the higher crate.
B	A force diagram for the lower crate.
C	A free-body diagram for the lower crate.
D	A force diagram for the higher crate.

Answer:

The correct choice is:

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A system of two crates is pulled up a rough inclined plane.

The cord joining the two crates is inextensible (it can't be stretched) and it is pulled tight.

Tlali draws a diagram to show all the forces acting on one of the crates.

This is the diagram that he draws:

Which one of the options below best describes the diagram that Tlali drew?

A	A force diagram for the higher crate.
B	A free-body diagram for the higher crate.
C	A free-body diagram for the lower crate.
D	A force diagram for the lower crate.

Answer:

The correct choice is:

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Adapted from DBE Nov 2015 Grade 11, P1, Q3
Physical constants · Physics formulas

A $\text{20}\ \text{kg}$ block is placed on a rough horizontal surface. A constant force $(\vec{F})$ pushes the block and the block moves across the surface at a constant speed as shown in the diagram below. The coefficient of kinetic friction $(\mu_{\text{k}})$ between the block and the surface is $\text{0,42}$ .

Draw a labelled free-body diagram showing all the forces acting on the block.

For each of the free-body diagrams below use the table of options (W to Z) to say if the diagram is correct or to explain why it is incorrect.

Answer:

Options
W	The diagram is correct!
X	The frictional force is missing.
Y	The normal force has the wrong direction.
Z	The frictional force has the wrong direction.

Diagram I

Diagram II

Diagram III

Diagram IV

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Adapted from DBE Nov 2015 Grade 11, P1, Q3
Physical constants · Physics formulas

A $\text{45}\ \text{kg}$ block is placed on a rough horizontal surface. A constant force $(\vec{F})$ pushes the block, but the block remains at rest as shown in the diagram below. The coefficient of static friction $(\mu_{\text{s}})$ between the block and the surface is $\text{0,57}$ . If the magnitude of the applied force were any larger, the block would begin to move.

Draw a labelled free-body diagram showing all the forces acting on the block.

For each of the free-body diagrams below use the table of options (W to Z) to say if the diagram is correct or to explain why it is incorrect.

Answer:

Options
W	The diagram is correct!
X	The normal force has the wrong length.
Y	The frictional force has the wrong direction.
Z	The applied force is in the wrong direction.

Diagram I

Diagram II

Diagram III

Diagram IV

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A string is used to hang a charged insulated sphere from the ceiling. An electrostatic force repels the charged sphere to the right. The sphere is in static equilibrium.

Phozisa draws the following free-body diagram to show all the forces acting on the charged sphere.

The diagram has the correct number of forces, but one of the forces is pointing in the wrong direction. Which force is incorrect?

A	$\vec{T}$
B	$\vec{F}_{\text{g}}$
C	$\vec{F}_{\text{elec}}$

Answer:

The force pointing in the wrong direction is:

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A system of two crates is pulled up a rough inclined plane.

Jabulile draws the following force diagram to show all the forces acting on the higher crate.

The diagram has the correct number of forces, but one of the forces is pointing in the wrong direction. Which force is incorrect?

A	$\vec{F}_{\text{g}}$
B	$\vec{T}$
C	$\vec{f}$
D	$\vec{F}_{\text{pull}}$
E	$\vec{F}_{\text{N}}$

Answer:

The force pointing in the wrong direction is:

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A crate is pushed to the left across a rough surface.

Chidinma tries to draw a force diagram to show all the forces acting on the crate.

This is the diagram that she draws:

The diagram has the correct number of forces, but there is a problem with the diagram! What mistake did Chidinma make?

A	The forces have not been labelled.
B	The forces have incorrect arrowheads.
C	A free-body diagram was drawn instead of a force diagram.
D	The tail of at least one force vector is in the wrong place.

Answer:

The mistake made was:

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An object is in a lift which is moving down at constant velocity.

Adeboye tries to draw a free-body diagram to show all the forces acting on the object.

This is the diagram that he draws:

The diagram has the correct number of forces, but there is a problem with the diagram! What mistake did Adeboye make?

A	The tail of at least one force vector is in the wrong place.
B	One of the forces is pointing in the wrong direction.
C	A force diagram was drawn instead of a free-body diagram.
D	The forces have incorrect arrowheads.

Answer:

The mistake made was:

6. Components and resultants of forces

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A gravitational force of $\vec{F}_{\text{g}} = \text{196}\ \text{N}$ is acting straight down on a block. The block is on an inclined plane with a slope inclined at an angle of $\text{34}\text{°}$ with the horizontal.

Calculate the components of the force due to gravity parallel and perpendicular to the slope.

INSTRUCTION: Round your answers to one decimal place.

Answer:

$\vec{F}_{\text{g},\parallel} =$ $\text{N}$

$\vec{F}_{\text{g},\perp} =$ $\text{N}$

numeric

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A gravitational force of $\vec{F}_{\text{g}} = \text{171}\ \text{N}$ is acting straight down on a block. The block is on an inclined plane with a slope inclined at an angle of $\text{31}\text{°}$ with the horizontal.

Calculate the components of the force due to gravity parallel and perpendicular to the slope.

INSTRUCTION: Round your answers to one decimal place.

Answer:

$\vec{F}_{\text{g},\parallel} =$ $\text{N}$

$\vec{F}_{\text{g},\perp} =$ $\text{N}$

numeric

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Five forces are acting on an object. The following diagram shows the scenario as seen from the side.

Three of the forces are aligned along the vertical axis. The other two forces are aligned along the horizontal axis.

Calculate:

The net force along the vertical axis.
The net force along the horizontal axis.

INSTRUCTIONS:

Give the magnitudes of both components to the nearest newton.
Use the drop-down menus to show the directions or to indicate if there is no direction.

Answer:

$\vec{F}_{\text{net,vertical}} =$ $\text{N}$ .
$\vec{F}_{\text{net,horizontal}} =$ $\text{N}$ .

numeric

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Five forces are acting on an object. The following diagram shows the scenario as seen from the side.

Three of the forces are aligned along the vertical axis. The other two forces are aligned along the horizontal axis.

Calculate:

The net force along the vertical axis.
The net force along the horizontal axis.

INSTRUCTIONS:

Give the magnitudes of both components to the nearest newton.
Use the drop-down menus to show the directions or to indicate if there is no direction.

Answer:

$\vec{F}_{\text{net,vertical}} =$ $\text{N}$ .
$\vec{F}_{\text{net,horizontal}} =$ $\text{N}$ .

numeric

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Box $\text{1}$ is connected to Box $\text{2}$ by a light inextensible cable. The same type of cable is attached to Box $\text{2}$ , run over a light frictionless pulley, and connected to a motor.

The following table contains possible expressions for the magnitude of the net force experienced by the two crates. Identify which expression belongs with each crate.

W	$F_{\text{motor}} - T - m_{2} g \cos \alpha$
X	$T - m_{1} g \sin \alpha$
Y	$F_{\text{motor}} - T - m_{2} g \sin \alpha$
Z	$T - m_{1} g \cos \alpha$

Answer:

The magnitude of the net force on the bottom box is given by .
The magnitude of the net force on the top box is given by .

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Block $\text{1}$ is connected to Block $\text{2}$ by a light inextensible rope. The same type of rope is attached to Block $\text{2}$ , run over a light frictionless pulley, and connected to a motor.

The following table contains possible expressions for the magnitude of the net force experienced by the two crates. Identify which expression belongs with each crate.

W	$T - m_{1} g \sin \alpha$
X	$T - m_{1} g \cos \alpha$
Y	$F_{\text{motor}} - T - m_{2} g \sin \alpha$
Z	$F_{\text{motor}} - T - m_{2} g \cos \alpha$

Answer:

The magnitude of the net force on the bottom block is given by .
The magnitude of the net force on the top block is given by .

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Megan is pulling an object across the floor with a force of $\text{150}\ \text{N}$ at an angle of $\text{32}°$ to the horizontal. The following diagram (which is not to scale) shows the scenario as seen from the side.

Resolve the pulling force into horizontal $(x)$ and vertical $(y)$ components.

INSTRUCTIONS:

Give magnitudes of the components.
Round both of your answers to two decimal places.

Answer:

The magnitudes of the components of the pulling force are:

$F_{x} =$ $\text{N}$

$F_{y} =$ $\text{N}$

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

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Riaan is pulling a crate across the floor with a force of $\text{280}\ \text{N}$ at an angle of $\text{20}°$ west of north. The following diagram (which is not to scale) shows the scenario as seen from above.

Resolve the pulling force into components to the north and west.

INSTRUCTIONS:

Give magnitudes of the components.
Round both of your answers to two decimal places.

Answer:

The magnitudes of the components of the pulling force are:

$F_{\text{north}} =$ $\text{N}$

$F_{\text{west}} =$ $\text{N}$

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

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Fadekemi is pulling a chest across the floor with a force $\vec{F}$ at an angle of $\text{38}°$ to the vertical. The following diagram (which is not to scale) shows the scenario as seen from the side.

The vertical component of the pulling force is $\text{258}\ \text{N}$ .

Calculate:

the magnitude of the applied pulling force.
the magnitude of the horizontal component of the pulling force.

INSTRUCTION: Round both of your answers to two decimal places.

Answer:

$F =$ $\text{N}$

$F_{x}=$ $\text{N}$

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

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Amy is pulling a block across the floor with a force $\vec{F}$ at an angle of $\text{32}°$ to the vertical. The following diagram (which is not to scale) shows the scenario as seen from the side.

The vertical component of the pulling force is $\text{153}\ \text{N}$ .

Calculate:

the magnitude of the applied pulling force.
the magnitude of the horizontal component of the pulling force.

INSTRUCTION: Round both of your answers to two decimal places.

Answer:

$F =$ $\text{N}$

$F_{x}=$ $\text{N}$

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

ID is: 3747 Seed is: 3001

Mike is pulling a block across the floor with a force $\vec{F}$ at an angle of $\alpha$ north of west. The following diagram (which is not to scale) shows the scenario as seen from above.

The component of the pulling force to the west is $\text{138}\ \text{N}$ and the component of the pulling force to the north is $\text{111}\ \text{N}$ .

Calculate:

the magnitude of the applied pulling force.
the angle that describes the direction of the applied pushing force.

INSTRUCTION: Round both of your answers to two decimal places.

Answer:

$F =$ $\text{N}$

$\alpha =$ $\text{°}$

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

ID is: 3747 Seed is: 8665

Hannah is pulling a crate across the floor with a force $\vec{F}$ at an angle of $\alpha$ east of south. The following diagram (which is not to scale) shows the scenario as seen from above.

The component of the pulling force to the south is $\text{233}\ \text{N}$ and the component of the pulling force to the east is $\text{140}\ \text{N}$ .

Calculate:

the magnitude of the applied pulling force.
the angle that describes the direction of the applied pushing force.

INSTRUCTION: Round both of your answers to two decimal places.

Answer:

$F =$ $\text{N}$

$\alpha =$ $\text{°}$

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

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ID is: 1501 Seed is: 570

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Five forces are acting on an object. The following diagram shows the scenario as seen from above.

Three of the forces are aligned along the east-west axis. The other two forces are aligned along the north-south axis.

Calculate the magnitude and direction of the net force exerted on the object.

INSTRUCTIONS:

Round both the magnitude and direction to two decimal places.
Specify the direction as an angle north of west.

Answer:

$\vec{F}_{\text{net}} =$ $\text{N}$ at $\text{°}$ north of west.

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

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Five forces are acting on a box. The following diagram shows the scenario as seen from above.

Three of the forces are aligned along the east-west axis. The other two forces are aligned along the north-south axis.

Calculate the magnitude and direction of the net force exerted on the box.

INSTRUCTIONS:

Round both the magnitude and direction to two decimal places.
Specify the direction as an angle south of west.

Answer:

$\vec{F}_{\text{net}} =$ $\text{N}$ at $\text{°}$ south of west.

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

ID is: 3524 Seed is: 6768

Anathi is moving house. He is pushing a table with mass $m$ down a ramp off the moving truck. The ramp is inclined at an angle $\alpha$ to the horizontal. The force has a magnitude $F$ and acts at an angle $\beta$ to the normal of the ramp as shown in the diagram below.

Write down expressions for the magnitude of the perpendicular component of the pushing force $(F_{\perp})$ as well as the magnitude of the perpendicular component of the gravitational force $(F_{\text{g,} \perp})$ .

TIP: Which components are calculated using $\cos$ and which are calculated using $\sin$ depends on the line from which the angle is measured (the horizontal, the vertical, from the normal of the ramp, from the ramp). Always go back to the definitions of the trig functions rather than trying to remember results like these.

You can use any of the following variables and trigonometric functions in your answers:

$\begin{aligned} β; m; α; g; F \\ \sin; \cos; \tan \end{aligned}$ $\begin{aligned} \beta\;\! ; \;\; m\;\! ; \;\; \alpha\;\! ; \;\; g\;\! ; \;\; F\\ \sin\;\! ; \;\; \cos\;\! ; \;\; \tan \end{aligned}$
INSTRUCTIONS:
- you can type a for the symbol $\alpha$
- you can type B for the symbol $\beta$
- put brackets around the angle of the trigonometric function e.g. type tan(a) for $\tan{\alpha}$
Answer:
The perpendicular component of the pushing force:
$F_{\perp} =$

The perpendicular component of the gravitational force:
$F_{\text{g,} \perp} =$

one-of
type(expression)
one-of
type(expression)
Anathi is pushing the table with a force of magnitude $\text{230}\ \text{N}$ at an angle $\text{67}\text{°}$ to the normal of the ramp. The table has a mass $\text{96}\ \text{kg}$ and the ramp is inclined at an angle $\text{40}\text{°}$ to the horizontal.

Calculate the components of the pushing force and the gravitational force that are perpendicular to the ramp.

INSTRUCTION: Round your answers to two decimal places.

Answer:
$\vec{F}_{\perp} =$
$\vec{F}_{\text{g,} \perp} =$

one-of
type(numeric.abserror(0.01))
numeric

ID is: 3524 Seed is: 1831

Nyakallo is moving house. She is pushing a cupboard with mass $m$ down a ramp off the moving truck. The ramp is inclined at an angle $\alpha$ to the vertical. The force has a magnitude $F$ and acts at an angle $\beta$ to the ramp as shown in the diagram below.

Write down expressions for the magnitude of the perpendicular component of the pushing force $(F_{y})$ as well as the magnitude of the perpendicular component of the gravitational force $(F_{\text{g,} y})$ .

TIP: Which components are calculated using $\cos$ and which are calculated using $\sin$ depends on the line from which the angle is measured (the horizontal, the vertical, from the normal of the ramp, from the ramp). Always go back to the definitions of the trig functions rather than trying to remember results like these.

You can use any of the following variables and trigonometric functions in your answers:

$\begin{aligned} m; g; β; α; F \\ \cos; \sin; \tan \end{aligned}$ $\begin{aligned} m\;\! ; \;\; g\;\! ; \;\; \beta\;\! ; \;\; \alpha\;\! ; \;\; F\\ \cos\;\! ; \;\; \sin\;\! ; \;\; \tan \end{aligned}$
INSTRUCTIONS:
- you can type a for the symbol $\alpha$
- you can type B for the symbol $\beta$
- put brackets around the angle of the trigonometric function e.g. type tan(a) for $\tan{\alpha}$
Answer:
The perpendicular component of the pushing force:
$F_{y} =$

The perpendicular component of the gravitational force:
$F_{\text{g,} y} =$

one-of
type(expression)
one-of
type(expression)
Nyakallo is pushing the cupboard with a force of magnitude $\text{220}\ \text{N}$ at an angle $\text{22}\text{°}$ to the ramp. The cupboard has a mass $\text{73}\ \text{kg}$ and the ramp is inclined at an angle $\text{46}\text{°}$ to the vertical.

Calculate the components of the pushing force and the gravitational force that are perpendicular to the ramp.

INSTRUCTION: Round your answers to two decimal places.

Answer:
$\vec{F}_{y} =$
$\vec{F}_{\text{g,} y} =$

one-of
type(numeric.abserror(0.01))
numeric

7. Newton's first law

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Kutlwano is driving a car along a dirt road. A rabbit crosses the road and Kutlwano immediately slams on the brakes and manages to stop in time. Fortunately, Kutlwano was wearing a seatbelt and so was unharmed.

Use appropriate physics principles to complete the paragraph below which explains the importance of seatbelts.

Answer:

Initially, Kutlwano and the car are travelling at the same velocity. When the driver slams on the brakes, a net force is exerted on the car which causes it to slow down.

If Kutlwano were not strapped in with a seatbelt, she experience this net force. According to Newton's first law of motion, she would keep moving at the same velocity due to her inertia. She would be moving than the car. She would be flung relative to the car. She might go through the windscreen and get severe injuries.

But, because Kutlwano is strapped in with a seatbelt, the seatbelt apply a net force on her. This will cause her to with the car.

ID is: 3789 Seed is: 9755

Ben is driving a car along a dirt road. A baboon crosses the road and Ben immediately slams on the brakes and manages to stop in time. Fortunately, Ben was wearing a seatbelt and so was unharmed.

Use appropriate physics principles to complete the paragraph below which explains the importance of seatbelts.

Answer:

Initially, Ben and the car are travelling at the same velocity. When the driver slams on the brakes, a net force is exerted on the car which causes it to slow down.

If Ben were not strapped in with a seatbelt, he experience this net force. According to Newton's first law of motion, he would keep moving at the same velocity due to his inertia. He would be moving than the car. He would be flung relative to the car. He might go through the windscreen and get severe injuries.

But, because Ben is strapped in with a seatbelt, the seatbelt apply a net force on him. This will cause him to with the car.

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A parcel is loose on the smooth back seat of a car. The driver of the car turns a corner sharply. The parcel is observed to slide to one side of the car.

Which one of the following statements could not be used as reason for why the parcel is observed to slide to the side?

A	The parcel experiences a zero net force.
B	The parcel has inertia and so resists a change in motion.
C	The parcel keeps moving in the same direction, with the same speed.
D	The influence of gravity on the parcel is reduced.

Answer: The incorrect reason is:

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Reabilwe is standing in a bus which is moving along a straight road. The bus suddenly speeds up. Reabilwe isn't holding onto anything and stumbles.

In which direction will Reabilwe stumble?

Answer:
Reabilwe will stumble .
Which one of the following gives the best reason why Reabilwe stumbles backward?

A Her velocity remains constant.
B It follows from Newton's third law of motion.
C The floor of the bus exerts a net force on her.
D Her inertia is conserved.

Answer:
The correct option is:

ID is: 3768 Seed is: 3328

Thandolwethu is standing in a bus which is moving along a straight road. The bus suddenly changes speed. Thandolwethu isn't holding onto anything and stumbles forward.

Did the bus speed up or slow down?

Answer:
The bus must have .
Which one of the following gives the best reason why Thandolwethu stumbles forward?

A Kinetic energy is always conserved.
B It follows from Newton's first law of motion.
C The floor of the bus exerts a net force on her.
D Her inertia is conserved.

Answer:
The correct option is:

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An object is loose on the smooth back seat of a car. The driver of the car turns a corner sharply. The object is observed to move to one side of the car.

Classify each of the following four statements as correct reasons or incorrect reasons for why the object is observed to move to the side.

Answer:

The mass of the object is smaller than that of the car.
The object keeps moving in the same direction, with the same speed.
The influence of gravity on the object is reduced.
The car has changed direction, but the object keeps moving in a straight line.

ID is: 3769 Seed is: 5468

A box is loose on the smooth back seat of a car. The driver of the car turns a corner sharply. The box is observed to slide to one side of the car.

Classify each of the following four statements as correct reasons or incorrect reasons for why the box is observed to slide to the side.

Answer:

The box keeps moving at a constant velocity.
The box has inertia and so resists a change in motion.
The influence of gravity on the box is reduced.
The mass of the box is smaller than that of the car.

ID is: 3290 Seed is: 7981

Four different learners were asked to state what they thought Newton’s first law of motion means. Three of the learners have incorrect interpretations and one has a correct interpretation.

Which one of the following statements is correct?

A	Objects change how they move because of their inertia.
B	Only if no net force acts on an object will its motion remain constant.
C	Objects tend to remain at rest which is the property of inertia.
D	Objects resist being in motion which is why they slow down.

Answer:

The answer is: .

ID is: 3290 Seed is: 1918

Four different learners were asked to state what they thought Newton’s first law of motion means. Three of the learners have incorrect interpretations and one has a correct interpretation.

Which one of the following statements is correct?

A	Objects move at a constant velocity only if they do not experience any forces.
B	Objects resist being in motion which is why they slow down.
C	Objects change how they move because of their inertia.
D	Only if no net force acts on an object will its motion remain constant.

Answer:

The answer is: .

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8. Newton's second law

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Adapted from DBE Nov 2015 & 2016 Grade 11, P1, Q4
Physical constants · Physics formulas

State Newton's second law of motion in words.

Answer:

When a resultant force acts on an object, the object will the with the magnitude of the resultant force and the mass of the object.

ID is: 3260 Seed is: 1848

Adapted from DBE Nov 2015 & 2016 Grade 11, P1, Q4
Physical constants · Physics formulas

State Newton's second law of motion in words.

Answer:

When is exerted on an object, the object will the with an acceleration the magnitude of the and inversely proportional to the mass of the object.

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The relationship $F_{\text{net}} = m a$ is an important equation in mechanics. It is the mathematical statement of Newton's second law of motion.

What does the symbol $m$ represent?

Answer:
The symbol $m$ represents .
What is the SI unit used to measure $a$ ?

Answer:
The SI unit used to measure $a$ is .

ID is: 3658 Seed is: 2318

The relationship $F_{\text{net}} = m a$ is an important equation in mechanics. It is the mathematical statement of Newton's second law of motion.

What does the symbol $a$ represent?

Answer:
The symbol $a$ represents .
What is the SI unit used to measure $F_{\text{net}}$ ?

Answer:
The SI unit used to measure $F_{\text{net}}$ is .

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A rocket has a mass of $\text{1,06} \times \text{10}^{\text{6}}\ \text{kg}$ and experiences a force of $\text{1,0388} \times \text{10}^{\text{7}}\ \text{N}$ due to gravity. The rocket is accelerating at $\text{11,98}\ \text{m·s$^{-2}$}$ .

What is the resultant force acting on the rocket?

INSTRUCTION: Write your answer in scientific notation and then round it to three decimal places.

Answer:
$\vec{F}_{\text{net}} =$ $\text{N}$

numeric
What driving force does the engine of the rocket need to exert on the rocket to maintain its acceleration?
INSTRUCTION:
- Use your unrounded answer from Question 1.
- Write your answer in scientific notation and then round it to three decimal places.
Answer:
$\vec{F}_{\text{drive}} =$ $\text{N}$

numeric

ID is: 1465 Seed is: 6040

A space shuttle has a mass of $\text{5,40} \times \text{10}^{\text{5}}\ \text{kg}$ and experiences a force of $\text{5,2920} \times \text{10}^{\text{6}}\ \text{N}$ due to gravity. The space shuttle is ignited and is launched with a driving force of $\text{2,139} \times \text{10}^{\text{7}}\ \text{N}$ upwards.

What is the resultant force acting on the space shuttle?

INSTRUCTION: Write your answer in scientific notation and then round it to three decimal places.

Answer:
$\vec{F}_{\text{net}} =$ $\text{N}$

numeric
What is the acceleration of the space shuttle?
INSTRUCTION:
- Use your unrounded answer from Question 1.
- Round your answer to two decimal places.
Answer:
$\vec{a} =$ $\text{m·s$^{-2}$}$

one-of
type(numeric.abserror(0.01))

ID is: 3657 Seed is: 2296

The relationship $F_{\text{net}} = ma$ is an important equation in mechanics. It is the mathematical statement of Newton's second law of motion.

For a fixed acceleration, what can we say about the relationship between net force and mass?

Answer:
Net force is mass.

Consider the options below and choose the one that represents the relationship between net force and mass symbolically:

A	$F_{\text{net}} = m$
B	$F_{\text{net}} \propto m$
C	$F_{\text{net}} \propto \dfrac{ 1 }{ m }$
D	$F_{\text{net}} > m$
E	$F_{\text{net}} < m$

Answer:

The correct option is .

Consider two systems with the same acceleration. The net force of the second system is 8 times smaller than the net force of the first system. How does the mass of the second system compare to the mass of the first system?

Answer:
The mass of the second system will be the mass of the first system.

ID is: 3657 Seed is: 6235

The relationship $F_{\text{net}} = ma$ is a useful equation in mechanics. It is the mathematical statement of Newton's second law of motion.

For a constant mass, what can we say about the relationship between acceleration and net force?

Answer:
Acceleration is net force.

Consider the options below and choose the one that represents the relationship between acceleration and net force symbolically:

A	$a > F_{\text{net}}$
B	$a \propto F_{\text{net}}$
C	$a = F_{\text{net}}$
D	$a \propto \dfrac{ 1 }{ F_{\text{net}} }$
E	$a < F_{\text{net}}$

Answer:

The correct option is .

Consider two systems with the same mass. The acceleration of the second system is 6 times smaller than the acceleration of the first system. How does the net force of the second system compare to the net force of the first system?

Answer:
The net force of the second system will be the net force of the first system.

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ID is: 3825 Seed is: 3352

Adapted from DBE Feb-Mar 2017 Grade 12, P1, Q2
Physical constants · Physics formulas

In the diagram below (not to scale), a small object of mass $\text{6}\ \text{kg}$ is sliding at a constant velocity of $\text{2,3}\ \text{m·s$^{-1}$}$ down a rough plane inclined at $\text{15}\text{°}$ to the horizontal surface.

At the bottom of the plane, the object continues sliding onto the rough horizontal surface and eventually comes to a stop.

The coefficient of kinetic friction between the object and the surface is the same for both inclined surface and the horizontal surface.

INSTRUCTIONS:

Round all final numerical answers to two decimal places.
You must use these values for any physical constants required in your calculations.

What is the magnitude of the net force acting on the object while it is on the slope?

Answer: The magnitude of the net force is $\text{N}$ .
numeric
Draw a labelled free-body diagram for the object while it is on the inclined plane. Then answer the questions that follow.
Answer:
1. How many forces are there in the free-body diagram?
2. Friction is .
3. There an applied force.
numeric
Calculate the:
1. Magnitude of the frictional force acting on the object while it is sliding down the inclined plane.
2. Coefficient of kinetic friction between the object and the surface.
3. Distance the object travels on the horizontal surface before it comes to a stop.
Answer:
1. $f_{\text{k}} =$
2. $\mu_{\text{k}} =$
3. $\Delta x =$
one-of
type(numeric.abserror(0.1))
one-of
type(numeric.abserror(0.01))
one-of
type(numeric.abserror(0.01))

ID is: 3825 Seed is: 6663

Adapted from DBE Feb-Mar 2017 Grade 12, P1, Q2
Physical constants · Physics formulas

In the diagram below (not to scale), a small object of mass $\text{9}\ \text{kg}$ is sliding at a constant velocity of $\text{3,5}\ \text{m·s$^{-1}$}$ down a rough plane inclined at $\text{22}\text{°}$ to the horizontal surface.

At the bottom of the plane, the object continues sliding onto the rough horizontal surface and eventually comes to a stop.

The coefficient of kinetic friction between the object and the surface is the same for both inclined surface and the horizontal surface.

INSTRUCTIONS:

Round all final numerical answers to two decimal places.
You must use these values for any physical constants required in your calculations.

What is the magnitude of the net force acting on the object while it is on the slope?

Answer: The magnitude of the net force is $\text{N}$ .
numeric
Draw a labelled free-body diagram for the object while it is on the inclined plane. Then answer the questions that follow.
Answer:
1. How many forces are there in the free-body diagram?
2. Friction is .
3. There an applied force.
numeric
Calculate the:
1. Magnitude of the frictional force acting on the object while it is sliding down the inclined plane.
2. Coefficient of kinetic friction between the object and the surface.
3. Distance the object travels on the horizontal surface before it comes to a stop.
Answer:
1. $f_{\text{k}} =$
2. $\mu_{\text{k}} =$
3. $\Delta x =$
one-of
type(numeric.abserror(0.1))
one-of
type(numeric.abserror(0.01))
one-of
type(numeric.abserror(0.01))

ID is: 4568 Seed is: 1826

ID is: 4568 Seed is: 3896

ID is: 1469 Seed is: 2565

A student experiences a gravitational force of $\text{774,2}\ \text{N}$ . He gets into a lift and steps onto a bathroom scale that is calibrated in newtons. When the lift is standing still the scale reads $\text{774,2}\ \text{N}$ . When the student steps into the lift it is on floor 9.

He pushes the button to go to another floor. As the lift moves he notes that the reading on the scale changes during his ride. He records three stages in his journey:

Stage 1 $\rightarrow$ For $\text{2}\ \text{seconds}$ immediately after the lift starts, the scale reads $\text{703,1}\ \text{N}$
Stage 2 $\rightarrow$ For a further $\text{3}\ \text{seconds}$ it reads $\text{774,2}\ \text{N}$
Stage 3 $\rightarrow$ For the final $\text{2}\ \text{seconds}$ it reads $\text{845,3}\ \text{N}$ .

Is the acceleration of the lift upward or downward in Stage 1?

TIP: In a test or exam you will be required to give reasons for your answer.

Answer:
The direction of the acceleration in Stage 1 is .
Calculate the resultant force acting on the student during Stage 3.
INSTRUCTION:
- Round your answer to one decimal place.
- Select the direction using the drop-down menu.
Answer:
$\vec{F}_{\text{net}} =$ $\text{N}$

one-of
type(numeric.abserror(0.1))

ID is: 1469 Seed is: 9510

A student experiences a gravitational force of $\text{1 029,0}\ \text{N}$ . He gets into a lift and steps onto a bathroom scale that is calibrated in newtons. When the lift is standing still the scale reads $\text{1 029,0}\ \text{N}$ . When the student steps into the lift it is on floor 5.

He pushes the button to go to another floor. As the lift moves he notes that the reading on the scale changes during his ride. He records three stages in his journey:

Stage 1 $\rightarrow$ For $\text{2}\ \text{seconds}$ immediately after the lift starts, the scale reads $\text{913,5}\ \text{N}$
Stage 2 $\rightarrow$ For a further $\text{3}\ \text{seconds}$ it reads $\text{1 029,0}\ \text{N}$
Stage 3 $\rightarrow$ For the final $\text{2}\ \text{seconds}$ it reads $\text{1 144,5}\ \text{N}$ .

Is the acceleration of the lift upward or downward in Stage 1?

TIP: In a test or exam you will be required to give reasons for your answer.

Answer:
The direction of the acceleration in Stage 1 is .
Calculate the resultant force acting on the student during Stage 1.
INSTRUCTION:
- Round your answer to one decimal place.
- Select the direction using the drop-down menu.
Answer:
$\vec{F}_{\text{net}} =$ $\text{N}$

one-of
type(numeric.abserror(0.1))

11. Newton's third law

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Newton's third law talks about action-reaction pairs. Four statements about action-reaction pairs are given to you below. For each of these statements, indicate if they are true or false.

1	Action-reaction pairs have the same magnitude.
2	Action-reaction pairs act on the same object.
3	Action-reaction pairs act in opposite directions.
4	Forces only sometimes occur in action-reaction pairs.

Answer:

Statement 1 is .

Statement 2 is .

Statement 3 is .

Statement 4 is .

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Newton's third law talks about action-reaction pairs. Four statements about action-reaction pairs are given to you below. For each of these statements, indicate if they are true or false.

1	Action-reaction pairs occur at different times; the reaction follows the action.
2	All forces occur in action-reaction pairs.
3	Action-reaction pairs arise as an interaction between two objects.
4	Action-reaction pairs have the same magnitude.

Answer:

Statement 1 is .

Statement 2 is .

Statement 3 is .

Statement 4 is .

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A mule is trying to pull a cart with no wheels across a rough dirt path, but the cart will not move.

The following diagram shows some of the forces involved in this scenario.

KEY:

$\vec{F}_{1}$ : normal force of the cart on the ground
$\vec{F}_{2}$ : normal force of the ground on the cart
$\vec{F}_{3}$ : gravitational force of the cart on the Earth
$\vec{F}_{4}$ : gravitational force of the Earth on the cart

Consider the following two pairs of forces:

(i)	$\vec{F}_{3}$ and $\vec{F}_{4}$
(ii)	$\vec{F}_{2}$ and $\vec{F}_{4}$

Which of the above pairs of forces are Newton's third law action-reaction pairs?

A	(i) only
B	(ii) only
C	Both (i) and (ii)
D	Neither (i) nor (ii)

Answer:

The correct option is: .

ID is: 3795 Seed is: 6818

A ball is falling down through the air at a constant velocity. As it falls it experiences air resistance.

The following diagram shows some of the forces involved in this scenario.

KEY:

$\vec{F}_{1}$ : air resistance of the air molecules on the ball
$\vec{F}_{2}$ : gravitational force of the ball on the Earth
$\vec{F}_{3}$ : air resistance of the ball on the air molecules
$\vec{F}_{4}$ : gravitational force of the Earth on the ball

Consider the following two pairs of forces:

(i)	$\vec{F}_{2}$ and $\vec{F}_{3}$
(ii)	$\vec{F}_{2}$ and $\vec{F}_{4}$

Which of the above pairs of forces are Newton's third law action-reaction pairs?

A	(i) only
B	(ii) only
C	Both (i) and (ii)
D	Neither (i) nor (ii)

Answer:

The correct option is: .

ID is: 3793 Seed is: 8946

A ball is falling down through the air at a constant velocity. As it falls it experiences air resistance.

Iminathi and Kevin draw a diagram and show some of the forces involved in this scenario.

KEY:

$\vec{F}_{1}$ : air resistance of the ball on the air molecules
$\vec{F}_{2}$ : gravitational force of the ball on the Earth
$\vec{F}_{3}$ : gravitational force of the Earth on the ball
$\vec{F}_{4}$ : air resistance of the air molecules on the ball

Iminathi says that $\vec{F}_{1}$ and $\vec{F}_{4}$ can cancel each other out. This is Iminathi's explanation of why she thinks that $\vec{F}_{1}$ and $\vec{F}_{4}$ can cancel each other out:

$\vec{F}_{1}$ and $\vec{F}_{4}$ form an action-reaction pair of forces. Forces in action-reaction pairs are always equal in magnitude and opposite in direction. So they will cancel each other out because their vector sum is zero. Which means that the net vertical force experienced by the ball will be zero.

Wow! That sounds pretty convincing, but Kevin disagrees and says that $\vec{F}_{1}$ and $\vec{F}_{4}$ cannot cancel each other out.

Determine whether Iminathi is correct or incorrect and give a reason from the table below.

$\vec{F}_{1}$ and $\vec{F}_{4}$ ...

A are not equal in magnitude
B do not both act on the ball
C are not opposite in direction
D are not an action-reaction pair

Answer:
Iminathi is because $\vec{F}_{1}$ and $\vec{F}_{4}$ .
Which pair of forces does cancel out to keep the ball in equilibrium?

Answer:
and will cancel each other out.

ID is: 3793 Seed is: 8900

A ball is falling down through the air at a constant velocity. As it falls it experiences air resistance.

Adaeze and Lethabo draw a diagram and show some of the forces involved in this scenario.

KEY:

$\vec{F}_{1}$ : air resistance of the air molecules on the ball
$\vec{F}_{2}$ : gravitational force of the ball on the Earth
$\vec{F}_{3}$ : air resistance of the ball on the air molecules
$\vec{F}_{4}$ : gravitational force of the Earth on the ball

Adaeze says that $\vec{F}_{1}$ and $\vec{F}_{3}$ can cancel each other out. This is Adaeze's explanation of why she thinks that $\vec{F}_{1}$ and $\vec{F}_{3}$ can cancel each other out:

$\vec{F}_{1}$ and $\vec{F}_{3}$ form an action-reaction pair of forces. Forces in action-reaction pairs are always equal in magnitude and opposite in direction. So they will cancel each other out because their vector sum is zero. Which means that the net vertical force experienced by the ball will be zero.

Wow! That sounds pretty convincing, but Lethabo disagrees and says that $\vec{F}_{1}$ and $\vec{F}_{3}$ cannot cancel each other out.

Determine whether Adaeze is correct or incorrect and give a reason from the table below.

$\vec{F}_{1}$ and $\vec{F}_{3}$ ...

A are not opposite in direction
B are not equal in magnitude
C do not both act on the ball
D are not an action-reaction pair

Answer:
Adaeze is because $\vec{F}_{1}$ and $\vec{F}_{3}$ .
Which pair of forces does cancel out to keep the ball in equilibrium?

Answer:
and will cancel each other out.

ID is: 3287 Seed is: 804

A body with mass $2m$ exerts a force of magnitude $F$ on a second body with mass $m$ . This is a net force which causes the second body to have an acceleration of magnitude $a$ .

Which one of the following statements is true regarding the force that the second object exerts on the first object and the acceleration experienced by the first object?

A	The force has magnitude $F$ and the acceleration has magnitude $\frac12a$ .
B	The force has magnitude $F$ and the acceleration has magnitude $a$ .
C	The force has magnitude $\frac12F$ and the acceleration has magnitude $\frac12a$ .
D	The force has magnitude $\frac12 F$ and the acceleration has magnitude $a$ .

Answer: The correct option is: .

ID is: 3287 Seed is: 5362

A body with mass $m$ exerts a force of magnitude $F$ on a second body with mass $5m$ . This is a net force which causes the second body to have an acceleration of magnitude $a$ .

Which one of the following statements is true regarding the force that the second object exerts on the first object and the acceleration experienced by the first object?

A	The force has magnitude $5 F$ and the acceleration has magnitude $a$ .
B	The force has magnitude $F$ and the acceleration has magnitude $a$ .
C	The force has magnitude $F$ and the acceleration has magnitude $5 a$ .
D	The force has magnitude $5F$ and the acceleration has magnitude $5a$ .

Answer: The correct option is: .

12. Forces between masses

13. Newton's universal law of gravitation

ID is: 3644 Seed is: 576

Adapted from DBE Nov 2015 & 2016 Grade 11, P1, Q5
Physical constants · Physics formulas

State Newton's universal law of gravitation in words.

Answer:

Every body in the universe every other body with a gravitational force that is the their masses and the of the distance between their centres.

ID is: 3644 Seed is: 5776

Adapted from DBE Nov 2015 & 2016 Grade 11, P1, Q5
Physical constants · Physics formulas

State Newton's universal law of gravitation in words.

Answer:

Every body in the universe every other body with a gravitational force that is the their masses and the of the distance between their centres.

ID is: 3807 Seed is: 8283

The following relationship is an important equation in mechanics:

\begin{matrix} F_{g} = \frac{G m_{1} m_{2}}{d^{2}} \end{matrix}

$\begin{array}{c} F_{\text{g}} = \dfrac{G m_{1}m_{2}}{d^{2}} \end{array}$

It is the mathematical form of Newton's universal law of gravitation.

What does the symbol $G$ stand for?

A magnitude of the gravitational force
B gravitational acceleration
C universal gravitational constant
D g-force

Answer:
The meaning of $G$ is .
What is the SI unit used to measure $d$ ?

Answer:
The SI unit used to measure $d$ is .

ID is: 3807 Seed is: 5861

The following relationship is an important equation in mechanics:

\begin{matrix} F_{g} = \frac{G m_{1} m_{2}}{d^{2}} \end{matrix}

$\begin{array}{c} F_{\text{g}} = \dfrac{G m_{1}m_{2}}{d^{2}} \end{array}$

It is the mathematical form of Newton's universal law of gravitation.

What does the symbol $F_{\text{g}}$ stand for?

A magnitude of the gravitational force
B gravitational acceleration
C g-force
D universal gravitational constant

Answer:
The meaning of $F_{\text{g}}$ is .
What is the SI unit in which we measure $m_{1}$ ?

Answer:
The SI unit in which we measure $m_{1}$ is .

ID is: 1466 Seed is: 3428

ID is: 1466 Seed is: 8215

ID is: 3320 Seed is: 499

Phetoho travels in a spaceship to Europa (a moon of Jupiter). He needs to know what kind of conditions to prepare for. In particular, he needs to know the average acceleration due to gravity on the surface of Europa in order to land safely. The mass of Europa is $\text{4,778} \times \text{10}^{\text{22}} \ \text{kg}$ and it has a radius of $\text{1 548,9} \ \text{km}$ .

Calculate the magnitude of the acceleration due gravity near the surface of Europa.

INSTRUCTIONS:

Round your answer to three decimal places.
You must use these values for any physical constants you might need.

Answer:

$g_{\text{Europa}}$ =

one-of

type(numeric.abserror(0.001))

ID is: 3320 Seed is: 43

Ekueme travels in a spaceship to Callisto (a moon of Jupiter). He needs to know what kind of conditions to prepare for. In particular, he needs to know the average acceleration due to gravity on the surface of Callisto in order to land safely. The mass of Callisto is $\text{1,080} \times \text{10}^{\text{23}} \ \text{kg}$ and it has a radius of $\text{2 424,4} \ \text{km}$ .

Calculate the magnitude of the acceleration due gravity near the surface of Callisto.

INSTRUCTIONS:

Round your answer to two decimal places.
You must use these values for any physical constants you might need.

Answer:

$g_{\text{Callisto}}$ =

one-of

type(numeric.abserror(0.01))

ID is: 1561 Seed is: 1168

Complete the definition/law or provide the term asked for:

TIP: You can't just make the statement true in a specific case. If it's a definition, then it needs to be generally true.

Newton's _______ law of motion states: If body A exerts a force on body B, then body B exerts a force of equal magnitude on body A, but in the opposite direction.

Answer:
one-of
type(string.nocase)
Newton's _______ law of motion states: If a resultant force acts on a body, it will cause the body to accelerate in the direction of the resultant force. The acceleration of the body will be directly proportional to the resultant force and inversely proportional to the mass of the body.

Answer:
one-of
type(string.nocase)

ID is: 1561 Seed is: 7388

ID is: 1542 Seed is: 900

ID is: 1542 Seed is: 6423

ID is: 3859 Seed is: 2835

In a distant galaxy, two planets, X and Y, are interacting gravitationally. Planet X has a mass of $\text{4,44} \times \text{10}^{\text{28}}\ \text{kg}$ and Planet Y has a mass of $\text{8,39} \times \text{10}^{\text{23}}\ \text{kg}$ . When the distance between them is $d$ , Planet X exerts a gravitational force of $\text{8,24} \times \text{10}^{\text{22}}\ \text{N}$ on Planet Y.

Determine the distance between the planets $(d)$ .
INSTRUCTIONS:
- Write your answer in scientific notation and then round it to two decimal places.
- Use these physical constants for any calculations.
Answer:
$d =$

numeric

What is the gravitational force exerted on Planet X by Planet Y?

A	The force points towards Y and away from X, and has a magnitude equal to $\text{8,24} \times \text{10}^{\text{22}}\ \text{N}$ .
B	The force points towards X and away from Y, and has a magnitude less than $\text{8,24} \times \text{10}^{\text{22}}\ \text{N}$ .
C	The force points towards X and away from Y, and has a magnitude equal to $\text{8,24} \times \text{10}^{\text{22}}\ \text{N}$ .
D	The force points towards Y and away from X, and has a magnitude less than $\text{8,24} \times \text{10}^{\text{22}}\ \text{N}$ .

Which of Newton's laws of motion should you use to answer the above question?

Answer:

The gravitational force of Y on X is .
The law to use is Newton's law of motion.

ID is: 3859 Seed is: 2522

In a distant galaxy, two asteroids, X and Y, are interacting gravitationally. Asteroid X has a mass of $\text{1,83} \times \text{10}^{\text{17}}\ \text{kg}$ and Asteroid Y has a mass $m_{\text{Y}}$ . When the distance between them is $\text{8,34} \times \text{10}^{\text{8}}\ \text{m}$ , Asteroid X exerts a gravitational force of $\text{6,35} \times \text{10}^{\text{4}}\ \text{N}$ on Asteroid Y.

Determine the mass of Asteroid Y $(m_{\text{Y}})$ .
INSTRUCTIONS:
- Write your answer in scientific notation and then round it to two decimal places.
- Use these physical constants for any calculations.
Answer:
$m_{\text{Y}} =$

numeric

What is the gravitational force exerted on Asteroid X by Asteroid Y?

A	The force points towards Y and away from X, and has a magnitude equal to $\text{6,35} \times \text{10}^{\text{4}}\ \text{N}$ .
B	The force points towards Y and away from X, and has a magnitude less than $\text{6,35} \times \text{10}^{\text{4}}\ \text{N}$ .
C	The force points towards X and away from Y, and has a magnitude less than $\text{6,35} \times \text{10}^{\text{4}}\ \text{N}$ .
D	The force points towards X and away from Y, and has a magnitude equal to $\text{6,35} \times \text{10}^{\text{4}}\ \text{N}$ .

Which of Newton's laws of motion should you use to answer the above question?

Answer:

The gravitational force of Y on X is .
The law to use is Newton's law of motion.

ID is: 3860 Seed is: 6307

Kelly is an astronomer and she is studying comets with different types of trajectory. One comet she is studying has an elliptical orbit around a star somewhere in the Milky Way.

NOTE: See how the tail of the comet points directly away from the star? The tail doesn't tell you anything about the direction of motion of the comet!

1. Identify the type of force experienced by the comet at Point A.
2. How does the force that the comet exerts on the star compare to the force that the star exerts on the comet at Point B?
Answer:
1. At Point A, the comet experiences force.
2. At Point B, the magnitude of the force that the comet exerts on the star is the magnitude of the force that the star exerts on the comet. These forces are in .
How does the acceleration experienced by the comet at Point C compare to the acceleration at Point D? Refer to the magnitudes as well as the directions of the accelerations as part of your answer.

Answer:
The magnitude of the acceleration at Point C is the magnitude of the acceleration at Point D.

of the accelerations point . At Point C the acceleration points and at Point D the acceleration points .

ID is: 3860 Seed is: 7220

Sindisiwe is an astronomer and she is studying comets with different types of trajectory. One comet she is studying has a parabolic orbit around a star somewhere in the Milky Way.

NOTE: See how the tail of the comet points directly away from the star? The tail doesn't tell you anything about the direction of motion of the comet!

1. Identify the type of force experienced by the comet at Point P.
2. How does the force that the comet exerts on the star compare to the force that the star exerts on the comet at Point Q?
Answer:
1. At Point P, the comet experiences force.
2. At Point Q, the magnitude of the force that the comet exerts on the star is the magnitude of the force that the star exerts on the comet. These forces are in .
How does the acceleration experienced by the comet at Point R compare to the acceleration at Point S? Refer to the magnitudes as well as the directions of the accelerations as part of your answer.

Answer:
The magnitude of the acceleration at Point R is the magnitude of the acceleration at Point S.

of the accelerations point . At Point R the acceleration points and at Point S the acceleration points .

ID is: 3861 Seed is: 1485

Adebanke is an astronomer and she is studying a planet which is orbiting a star in the Milky Way galaxy. The planet is a massive gas giant and has a mass of $\text{6,54} \times \text{10}^{\text{28}}\ \text{kg}$ and its parent star has a mass of $\text{2,95} \times \text{10}^{\text{30}}\ \text{kg}$ . Adebanke plots the position of the planet and its star on a Cartesian plane. The origin of the Cartesian plane is located at the centre of the star. Adebanke uses this graph to establish that the planet traces out an elliptical orbit around the sun.

On a particular date, Adebanke observes the planet at the coordinate $(\text{78,7} ; -\text{63,8})$ $\text{million km}$ relative to the sun.

Calculate the gravitational force that the planet exerts on the star.

INSTRUCTIONS:

Give the magnitude of the force to two decimal places, in scientific notation.
Give the direction of the force, to one decimal place, as an angle measured anti-clockwise from the positive $x$ -axis.
Use these values for any physical constants you might need.

Answer:

$\vec{F}_{\text{g}} =$ at $\text{°}$ anti-clockwise from the positive $x$ -axis.

TIP: Do not give the angle as a bearing! You need to work with the angle the same way you would in maths.

numeric

one-of

type(numeric.abserror(0.1))

ID is: 3861 Seed is: 4000

Aisha is an astronomer and she is studying a planet which is orbiting a star in the Milky Way galaxy. The planet is a massive gas giant and has a mass of $\text{9,42} \times \text{10}^{\text{27}}\ \text{kg}$ and its parent star has a mass of $\text{6,85} \times \text{10}^{\text{31}}\ \text{kg}$ . Aisha plots the position of the planet and its star on a Cartesian plane. The origin of the Cartesian plane is located at the centre of the star. Aisha uses this graph to establish that the planet traces out an elliptical orbit around the sun.

On a particular date, Aisha observes the planet at the coordinate $(-\text{858} ; -\text{437})$ $\text{million km}$ relative to the sun.

Calculate the gravitational force that the planet exerts on the star.

INSTRUCTIONS:

Give the magnitude of the force to two decimal places, in scientific notation.
Give the direction of the force, to one decimal place, as an angle measured anti-clockwise from the positive $x$ -axis.
Use these values for any physical constants you might need.

Answer:

$\vec{F}_{\text{g}} =$ at $\text{°}$ anti-clockwise from the positive $x$ -axis.

TIP: Do not give the angle as a bearing! You need to work with the angle the same way you would in maths.

numeric

one-of

type(numeric.abserror(0.1))

ID is: 3827 Seed is: 1843

Thandolwethu is on holiday in Sydney (in Australia) which is at an altitude of $\text{37}\ \text{m}$ above sea-level. She climbs the stairs to the top of the Sydney Tower, which has a total height of $\text{309}\ \text{m}$ above the ground. Thandolwethu has a mass of $\text{78}\ \text{kg}$ .

The mass of the Earth is $\text{5,972} \times \text{10}^{\text{24}}\ \text{kg}$ . The distance from the centre of the Earth to sea-level is $\text{6 371}\ \text{km}$ .

INSTRUCTIONS:

Round all numerical answers to five decimal places.
You cannot assume that $g = \text{9,8}\ \text{m·s$^{-2}$}$ anywhere in this question!

What is Thandolwethu's weight at the bottom of the Sydney Tower?

Answer:
Thandolwethu's weight is at the bottom.

one-of
type(numeric.abserror(1e-05))
Thandolwethu has been studying physics during her holiday and knows that the gravitational force decreases in magnitude as distance increases. She wonders what fraction of her weight she will have lost during her climb up the Sydney Tower.
1. What percentage of her weight does Thandolwethu lose when climbing to the top of the Sydney Tower?
2. Does Thandolwethu lose mass when climbing to the top of the Sydney Tower?
Answer:
1. Thandolwethu loses $\text{%}$ of her weight.
2. Thandolwethu lose any mass.
one-of
type(numeric.abserror(5e-05))

ID is: 3827 Seed is: 8230

Ikenna is on holiday in Kuala Lumpur (in Malaysia) which is at an altitude of $\text{37}\ \text{m}$ above sea-level. He climbs the stairs to the top of the Menara Telekom (a very tall building), which has a total height of $\text{310}\ \text{m}$ above the ground. Ikenna has a mass of $\text{81}\ \text{kg}$ .

The mass of the Earth is $\text{5,972} \times \text{10}^{\text{24}}\ \text{kg}$ . The distance from the centre of the Earth to sea-level is $\text{6 371}\ \text{km}$ .

INSTRUCTIONS:

Round all numerical answers to five decimal places.
You cannot assume that $g = \text{9,8}\ \text{m·s$^{-2}$}$ anywhere in this question!

What is Ikenna's weight at the bottom of the Menara Telekom?

Answer:
Ikenna's weight is at the bottom.

one-of
type(numeric.abserror(1e-05))
Ikenna has been studying physics during his holiday and knows that the gravitational force decreases in magnitude as distance increases. He wonders what fraction of his weight he will have lost during his climb up the Menara Telekom.
1. What percentage of his weight does Ikenna lose when climbing to the top of the Menara Telekom?
2. Does Ikenna lose mass when climbing to the top of the Menara Telekom?
Answer:
1. Ikenna loses $\text{%}$ of his weight.
2. Ikenna lose any mass.
one-of
type(numeric.abserror(5e-05))

ID is: 3826 Seed is: 3040

A space rocket of mass $\text{21 100}\ \text{kg}$ is orbiting Dione (a moon of Saturn) at a height of $\text{220}\ \text{km}$ above the surface of Dione. The rocket has switched off its engines and is effectively in free-fall as it orbits in a circular path.

Dione has a mass of $\text{1,10} \times \text{10}^{\text{21}}\ \text{kg}$ and a radius of $\text{5,614} \times \text{10}^{\text{2}}\ \text{km}$ .

Calculate the force of gravity experienced by the rocket.
INSTRUCTIONS:
- Give your answer rounded to three decimal places in scientific notation.
- You must use these values for any physical constants you might need.
Answer:
$\vec{F}_{\text{g}} =$

numeric
Calculate the acceleration of the rocket as it orbits Dione.
INSTRUCTIONS:
- Round your answer to three decimal places.
- Where necessary, use unrounded values from Question 1.
Answer:
$\vec{a} =$ .

one-of
type(numeric.abserror(0.001))

The rocket orbits Dione with a constant speed. How is it possible for the rocket to have a non-zero acceleration and maintain a constant speed?

A	The rocket constantly needs to fire the engines to brake to maintain a constant speed.
B	It's not possible. The acceleration of the rocket must be zero.
C	The acceleration changes the direction of motion, but not the speed of the rocket.
D	It's not possible. The rocket's speed will increase.

Answer:

The correct option is:

ID is: 3826 Seed is: 289

A space rocket of mass $\text{23 500}\ \text{kg}$ is orbiting Umbriel (a moon of Uranus) at a height of $\text{310}\ \text{km}$ above the surface of Umbriel. The rocket has switched off its engines and is effectively in free-fall as it orbits in a circular path.

Umbriel has a mass of $\text{1,20} \times \text{10}^{\text{21}}\ \text{kg}$ and a radius of $\text{5,847} \times \text{10}^{\text{2}}\ \text{km}$ .

Calculate the force of gravity experienced by the rocket.
INSTRUCTIONS:
- Give your answer rounded to three decimal places in scientific notation.
- You must use these values for any physical constants you might need.
Answer:
$\vec{F}_{\text{g}} =$

numeric
Calculate the acceleration of the rocket as it orbits Umbriel.
INSTRUCTIONS:
- Round your answer to four decimal places.
- Where necessary, use unrounded values from Question 1.
Answer:
$\vec{a} =$ .

one-of
type(numeric.abserror(0.0001))

The rocket orbits Umbriel with a constant speed. How is it possible for the rocket to have a non-zero acceleration and maintain a constant speed?

A	It's not possible. The rocket's speed will increase.
B	It's not possible. The acceleration of the rocket must be zero.
C	The rocket constantly needs to fire the engines to brake to maintain a constant speed.
D	The acceleration changes the direction of motion, but not the speed of the rocket.

Answer:

The correct option is:

14. Weight and mass

ID is: 3798 Seed is: 287

ID is: 3798 Seed is: 4940

ID is: 3799 Seed is: 652

Mass and weight are related to each other, but they are different quantities in physics.

The lists below summarise some important differences between mass and weight. But each list is missing two pieces of information! Complete the lists by selecting the correct choices.

Answer:

Mass:

is an amount of
has the symbol
is measured in SI units of $\text{kg}$
does not depend on location

Weight:

is an amount of
has the symbol
is measured in SI units of $\text{N}$
does depend on location

ID is: 3799 Seed is: 1636

Mass and weight are related to each other, but they are different quantities in physics.

The lists below summarise some important differences between mass and weight. But each list is missing two pieces of information! Complete the lists by selecting the correct choices.

Answer:

Mass:

is an amount of matter
has the symbol
is measured in SI units of $\text{kg}$
depend on location

Weight:

is an amount of force
has the symbol
is measured in SI units of $\text{N}$
depend on location

ID is: 3656 Seed is: 4129

The relationship $F_{\text{g}} = m g$ is an important equation in mechanics.

What does the symbol $m$ stand for?

Answer:
The symbol $m$ stands for .
What is the SI unit in which we measure $F_{\text{g}}$ ?

Answer:
The SI unit in which we measure $F_{\text{g}}$ is .

ID is: 3656 Seed is: 8506

The relationship $F_{\text{g}} = m g$ is a useful equation in mechanics.

What does the symbol $g$ stand for?

Answer:
The symbol $g$ stands for .
What is the SI unit used to measure $F_{\text{g}}$ ?

Answer:
The SI unit used to measure $F_{\text{g}}$ is .

ID is: 3646 Seed is: 7827

ID is: 3646 Seed is: 6128

ID is: 3637 Seed is: 5402

ID is: 3637 Seed is: 1130

ID is: 3813 Seed is: 6306

A box on the Earth's surface has a mass of $\text{56}\ \text{kg}$ .

Calculate the weight of the box.

INSTRUCTIONS:

Round your answer to one decimal place.
Choose the correct unit for weight from the drop-down menu.
Use any physical constants that you may need as listed here.

Answer: The weight of the box is .

one-of

type(numeric.abserror(0.1))

ID is: 3813 Seed is: 21

A box on the Earth's surface has a mass of $\text{77}\ \text{kg}$ .

Calculate the weight of the box.

INSTRUCTIONS:

Round your answer to one decimal place.
Choose the correct unit for weight from the drop-down menu.
Use any physical constants that you may need as listed here.

Answer: The weight of the box is .

one-of

type(numeric.abserror(0.1))

ID is: 3645 Seed is: 6089

Match the descriptions in the table below to the concepts of true weight, apparent weight, and weightlessness.

X	Always equal to $mg$ , where $m$ is the mass of an object and $g$ is the local acceleration due to gravity.
Y	A feeling experienced when the only force acting on the body is the gravitational force.
Z	The weight felt or perceived by a body.

Answer:

True weight:
Apparent weight:
Weightlessness:

ID is: 3645 Seed is: 6570

Match the descriptions in the table below to the concepts of true weight, apparent weight, and weightlessness.

X	The force a body exerts on the surface it rests on.
Y	Always equal to $mg$ , where $m$ is the mass of an object and $g$ is the local acceleration due to gravity.
Z	A feeling experienced when a body is in free-fall.

Answer:

True weight:
Apparent weight:
Weightlessness:

ID is: 3427 Seed is: 3325

Monique is exploring Dione (a moon of Saturn). She is expecting a container of supplies with a mass of $\text{2 130}\ \text{kg}$ to be delivered to Dione so she can continue her mission. Dione has a gravitational acceleration of $\text{0,23}\ \text{m·s$^{-2}$}$ .

Calculate the gravitational force acting on the container on Dione.

INSTRUCTIONS:

Round your answer to two decimal places.
You must use these values for any physical constants you might need.

Answer:

$F_{\text{g,Dione}} =$

one-of

type(numeric.abserror(0.01))

ID is: 3427 Seed is: 555

Fadekemi is exploring Ganymede (a moon of Jupiter). She is expecting a package of supplies with a mass of $\text{6 000}\ \text{kg}$ to be delivered to Ganymede so she can continue her mission. Ganymede has a gravitational acceleration of $\text{1,43}\ \text{m·s$^{-2}$}$ .

Calculate the gravitational force acting on the package on Ganymede.

INSTRUCTIONS:

Round your answer to two decimal places.
You must use these values for any physical constants you might need.

Answer:

$F_{\text{g,Ganymede}} =$

one-of

type(numeric.abserror(0.01))

ID is: 3475 Seed is: 4465

Lami wants to know how the solar system evolved to its current state. While exploring the solar system, she decides to land on Europa (a moon of Jupiter).

In order to land the spacecraft safely on the surface of Europa, Lami needs to gather some additional information. The mass of Europa is $\text{4,785} \times \text{10}^{\text{22}}\ \text{kg}$ and it has a radius of $\text{1 565,7}\ \text{km}$ .

Calculate the magnitude of the acceleration due gravity near the surface of Europa.
INSTRUCTION:
- Round your answer to two decimal places.
- Use the values for any physical constants you may need, as listed here.
Answer:
$\text{g}_{\text{Europa}} =$

one-of
type(numeric.abserror(0.01))
After safely landing on Europa, Lami analyses the composition of an interesting section of bedrock. The section of bedrock has a mass of $\text{20 000}\ \text{kg}$ .

Calculate the weight of the section of bedrock.
INSTRUCTION:
- Where applicable, use unrounded values from Question 1.
- Round your answer to the nearest $\text{100}\ \text{N}$ .
Answer:
$F_{\text{g}} =$

numeric

ID is: 3475 Seed is: 5414

Melanie wants to know how the solar system evolved to its current state. While exploring the solar system, she decides to land on Mercury (a planet).

In order to land the spacecraft safely on the surface of Mercury, Melanie needs to gather some additional information. The mass of Mercury is $\text{3,278} \times \text{10}^{\text{23}}\ \text{kg}$ and it has a radius of $\text{2 460,6}\ \text{km}$ .

Calculate the magnitude of the acceleration due gravity near the surface of Mercury.
INSTRUCTION:
- Round your answer to two decimal places.
- Use the values for any physical constants you may need, as listed here.
Answer:
$\text{g}_{\text{Mercury}} =$

one-of
type(numeric.abserror(0.01))
After safely landing on Mercury, Melanie analyses the composition of an interesting boulder. The boulder has a weight of $\text{134 200}\ \text{N}$ .

Calculate the mass of the boulder.
INSTRUCTION:
- Where applicable, use unrounded values from Question 1.
- Round your answer to the nearest $\text{100}\ \text{kg}$ .
Answer:
$m =$

numeric

ID is: 3862 Seed is: 1653

Gabisile is an astronaut. She performs an experiment to see how her weight varies from place to place in the solar system. She takes her mom's bathroom scale and sets off in her spaceship to measure her weight near the surface of different planets, moons, and asteroids in the solar system.

She obtains the following results:

Location	Weight ( $\text{N}$ )
Earth	$\text{768,4}$
Saturn (a planet)	$\text{818,5}$
Uranus (a planet)	$\text{695,1}$
Tethys (a moon of Saturn)	$\text{11,4}$
Ceres (an asteroid and dwarf planet)	$\text{21,9}$

Identify the independent, the dependent, and a fixed variable in Gabisile's investigation:

Answer:

Independent
Dependent
Fixed

Here is Gabisile's data table again:

Location	Weight ( $\text{N}$ )
Earth	$\text{768,4}$
Saturn (a planet)	$\text{818,5}$
Uranus (a planet)	$\text{695,1}$
Tethys (a moon of Saturn)	$\text{11,4}$
Ceres (an asteroid and dwarf planet)	$\text{21,9}$

Use this table to calculate:

Gabisile's mass $(m)$ .
The local acceleration due to gravity on Saturn $(g_{\text{Saturn}})$ .
The mass of Saturn $(M_{\text{Saturn}})$ if its radius is $\text{6,027} \times \text{10}^{\text{7}}\ \text{m}$ .

INSTRUCTIONS:

Round all answers to two decimal places.
The mass of Saturn should be in scientific notation.
You must use these values for any physical constants required in your calculations.
You might find some of these physics formulas useful.

Answer:

$m =$
$g_{\text{Saturn}} =$
$M_{\text{Saturn}} =$

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.scientific.abserror(1e+24))

Gabisile uses the data from the table to produce a graph. What type of graph should Gabisile use? Give a reason for your answer.

Answer: Gabisile should use a because the data is and make up a whole.

ID is: 3862 Seed is: 9838

Hannelie is an astronaut. She performs an experiment to see how her weight varies from place to place in the solar system. She takes her dad's bathroom scale and sets off in her spaceship to measure her weight near the surface of different planets, moons, and asteroids in the solar system.

She obtains the following results:

Location	Weight ( $\text{N}$ )
Earth	$\text{705,7}$
Ceres (an asteroid and dwarf planet)	$\text{20,2}$
Mars (a planet)	$\text{267,4}$
Venus (a planet)	$\text{638,5}$
Rhea (a moon of Saturn)	$\text{19,1}$

Identify the independent, the dependent, and a fixed variable in Hannelie's investigation:

Answer:

Independent
Dependent
Fixed

Here is Hannelie's data table again:

Location	Weight ( $\text{N}$ )
Earth	$\text{705,7}$
Ceres (an asteroid and dwarf planet)	$\text{20,2}$
Mars (a planet)	$\text{267,4}$
Venus (a planet)	$\text{638,5}$
Rhea (a moon of Saturn)	$\text{19,1}$

Use this table to calculate:

Hannelie's mass $(m)$ .
The local acceleration due to gravity on Rhea $(g_{\text{Rhea}})$ .
The radius of Rhea $(R_{\text{Rhea}})$ if its mass is $\text{2,317} \times \text{10}^{\text{21}}\ \text{kg}$ .

INSTRUCTIONS:

Round all answers to two decimal places.
The radius of Rhea should be in scientific notation.
You must use these values for any physical constants required in your calculations.
You might find some of these physics formulas useful.

Answer:

$m =$
$g_{\text{Rhea}} =$
$R_{\text{Rhea}} =$

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.abserror(0.01))

one-of

type(numeric.scientific.abserror(1e+03))

Hannelie uses the data from the table to produce a graph. What type of graph should Hannelie use? Give a reason for your answer.

Answer: Hannelie should use a because the data is and make up a whole.

ID is: 3814 Seed is: 7283

A girl is sitting in a roller coaster which is accelerating downwards.

How does the apparent weight of the girl compare to her true weight?
Does the girl experience weightlessness?

Answer:

The girl's apparent weight is her true weight.
The girl experience weightlessness.

ID is: 3814 Seed is: 5512

An astronaut is standing in a rocket which is accelerating downwards (towards the surface of the Earth) with an acceleration less than $\text{9,8}\ \text{m·s$^{-2}$}$ .

How does the apparent weight of the astronaut compare to her true weight?
Does the astronaut experience weightlessness?

Answer:

The astronaut's apparent weight is her true weight.
The astronaut experience weightlessness.

15. Proportional reasoning with gravity

ID is: 1541 Seed is: 7077

ID is: 1541 Seed is: 3710

ID is: 1492 Seed is: 849

ID is: 1492 Seed is: 8408

ID is: 1477 Seed is: 5720

ID is: 1477 Seed is: 7758

ID is: 1479 Seed is: 5568

ID is: 1479 Seed is: 1726

ID is: 3808 Seed is: 3252

Two moons are gravitationally attracted to each other in deep space.

Consider a second scenario where, compared to the first scenario,

the distance between the two moons is smaller,
and both masses are larger.

The above images are not perfectly to scale.

How will the gravitational force between the two moons in each scenario compare?

The gravitational force in the second scenario will be:

A	stronger
B	weaker
C	the same
D	impossible to know

Answer: The correct option is:

ID is: 3808 Seed is: 4183

Two moons are gravitationally attracted to each other in deep space.

Consider a second scenario where, compared to the first scenario,

the distance between the two moons is greater,
and one mass is smaller while the other mass is the same.

The above images are not perfectly to scale.

How will the gravitational force between the two moons in each scenario compare?

The gravitational force in the second scenario will be:

A	stronger
B	weaker
C	the same
D	impossible to know

Answer: The correct option is:

ID is: 3659 Seed is: 4953

The relationship $F_{\text{g}} = mg$ is an important equation in mechanics. It is the mathematical statement that shows the relationship between weight, mass, and a planet's local gravitational acceleration.

Consider two systems on the same planet (they have the same local gravitational acceleration).

What can we say about the relationship between the weight of each system and the mass?

Answer:
The weight is the mass.

Consider the options below and choose the one that represents the relationship between weight and mass symbolically:

A	$F_{\text{g}} \propto \dfrac{ 1 }{ m }$
B	$F_{\text{g}} \propto m$
C	$F_{\text{g}} > m$
D	$F_{\text{g}} < m$
E	$F_{\text{g}} = m$

Answer:

The correct option is .

The mass of the second system is $\text{8}$ times bigger than the mass of the first system. How does the weight of the second system compare to the weight of the first system?

Answer:
The weight of the second system will be the weight of the first system.

ID is: 3659 Seed is: 5624

The relationship $F_{\text{g}} = mg$ is a useful equation in mechanics. It is the mathematical statement that shows the relationship between weight, mass, and a planet's local gravitational acceleration.

Consider two objects with the same mass on different planets.

What can we say about the relationship between the weight of each object and the local gravitational acceleration?

Answer:
The weight is the local gravitational acceleration.

Consider the options below and choose the one that represents the relationship between weight and local gravitational acceleration symbolically:

A	$F_{\text{g}} \propto \dfrac{ 1 }{ g }$
B	$F_{\text{g}} < g$
C	$F_{\text{g}} = g$
D	$F_{\text{g}} \propto g$
E	$F_{\text{g}} > g$

Answer:

The correct option is .

The gravitational acceleration of the second planet is $\text{7}$ times smaller than the gravitational acceleration of the first planet. How does the weight of the second object compare to the weight of the first object?

Answer:
The weight of the second object will be the weight of the first object.

ID is: 3321 Seed is: 8975

Two stars (H and J) are in deep space. H has mass $m$ and J has mass $m$ . The distance between their centres of mass is $d$ . The gravitational force experienced by star J is $F$ .

Consider a different system of two stars in which:

the mass of the first star is bigger than the mass of star H by a factor of $\text{3}$ ,
the mass of the second star is bigger than the mass of star J by a factor of $\text{2}$ ,
and the distance between the two stars is $\dfrac{\text{1}}{\text{2}}$ $d$ .

What is the magnitude of the gravitational force experienced between these two stars in terms of the original force $F$ ?

A	$\dfrac{\text{3}}{\text{2}}F$
B	$\text{3}F$
C	$\text{12}F$
D	$\text{24}F$

Answer:

The correct option is:

ID is: 3321 Seed is: 6844

Two planets (U and V) are in deep space. U has mass $m$ and V has mass $\text{4}$ $m$ . The distance between their centres of mass is $d$ . The gravitational force experienced by planet V is $F$ .

Consider a different system of two planets in which:

the mass of the first planet is the same as the mass of planet U,
the mass of the second planet is bigger than the mass of planet V by a factor of $\text{4}$ ,
and the distance between the two planets is $\dfrac{\text{1}}{\text{3}}$ $d$ .

What is the magnitude of the gravitational force experienced between these two planets in terms of the original force $F$ ?

A	$\dfrac{\text{16}}{\text{9}}F$
B	$\dfrac{\text{16}}{\text{3}}F$
C	$\dfrac{\text{4}}{\text{3}}F$
D	$\text{36}F$

Answer:

The correct option is:

ID is: 1476 Seed is: 2713

ID is: 1476 Seed is: 6264

ID is: 1540 Seed is: 741

ID is: 1540 Seed is: 772

ID is: 1543 Seed is: 5627

ID is: 1543 Seed is: 7233

ID is: 3319 Seed is: 1474

Two asteroids (K and L) are in deep space. K has mass $m$ and L has mass $m$ . The distance between their centres of mass is $d$ . The gravitational force experienced by asteroid L is $F$ .

Consider a different system of two asteroids in which:

the mass of the first asteroid is bigger than the mass of asteroid K by a factor of $\text{2}$ ,
the mass of the second asteroid is bigger than the mass of asteroid L by a factor of $\text{3}$ ,
and the distance between the two asteroids is $\text{2}$ $d$ .

What is the magnitude of the gravitational force experienced between these two asteroids in terms of the original force $F$ ?

INSTRUCTION: Write your answer as a non-decimal fraction or as a whole number (whichever is more appropriate).

Answer:

$F_{\text{new}} =$ $F$

fraction

ID is: 3319 Seed is: 6102

Two moons (U and V) are in deep space. U has mass $m$ and V has mass $\text{4}$ $m$ . The distance between their centres of mass is $d$ . The gravitational force experienced by moon V is $F$ .

Consider a different system of two moons in which:

the mass of the first moon is bigger than the mass of moon U by a factor of $\text{3}$ ,
the mass of the second moon is bigger than the mass of moon V by a factor of $\text{4}$ ,
and the distance between the two moons is $d$ .

What is the magnitude of the gravitational force experienced between these two moons in terms of the original force $F$ ?

INSTRUCTION: Write your answer as a non-decimal fraction or as a whole number (whichever is more appropriate).

Answer:

$F_{\text{new}} =$ $F$

fraction

ID is: 1480 Seed is: 1787

ID is: 1480 Seed is: 8462

ID is: 4015 Seed is: 3094

ID is: 4015 Seed is: 6672

A	increases the normal force.
B	decreases the normal force.
C	increases the coefficient of kinetic friction.
D	decreases the coefficient of kinetic friction.
E	does not change either the normal force or the coefficient of kinetic friction.

A	increases the normal force.
B	decreases the normal force.
C	increases the coefficient of kinetic friction.
D	decreases the coefficient of kinetic friction.
E	does not change either the normal force or the coefficient of kinetic friction.

A	$f_{\text{s}}^{\text{max}} > F_{\text{N}}$
B	$f_{\text{s}}^{\text{max}} < F_{\text{N}}$
C	$f_{\text{s}}^{\text{max}} \propto \dfrac{ 1 }{ F_{\text{N}} }$
D	$f_{\text{s}}^{\text{max}} = F_{\text{N}}$
E	$f_{\text{s}}^{\text{max}} \propto F_{\text{N}}$

A	$f_{\text{s}}^{\text{max}} = \mu_{\text{s}}$
B	$f_{\text{s}}^{\text{max}} < \mu_{\text{s}}$
C	$f_{\text{s}}^{\text{max}} \propto \mu_{\text{s}}$
D	$f_{\text{s}}^{\text{max}} > \mu_{\text{s}}$
E	$f_{\text{s}}^{\text{max}} \propto \dfrac{ 1 }{ \mu_{\text{s}} }$

A	the normal force
B	the magnitude of the pulling force
C	the tension in the string
D	the table surface used

A	$f_{\text{k}} = \dfrac{{\mu}_{\text{k}}}{F_{\text{N}}}$
B	$f_{\text{k}} = {\mu}_{\text{k}} F_{\text{N}}$
C	$f_{\text{k}} = \dfrac{F_{\text{N}}}{{\mu}_{\text{k}}}$

A	${\mu}_{\text{s}} = \dfrac{F_{\text{N}}}{{f_{\text{s}}}^{\text{max}}}$
B	${\mu}_{\text{s}} = F_{\text{N}} {f_{\text{s}}}^{\text{max}}$
C	${\mu}_{\text{s}} = \dfrac{{f_{\text{s}}}^{\text{max}}}{F_{\text{N}}}$

$M\,(\text{kg})$	$F_{\text{pull}}\,(\text{N})$
$\text{0,57}$	$\text{2,6}$
$\text{0,67}$	$\text{2,7}$
$\text{0,77}$	$\text{3,1}$
$\text{0,87}$	$\text{3,7}$
$\text{0,97}$	$\text{4,2}$

A	Calculate the gradient of a graph of the normal force plotted against the maximum static frictional force
B	Calculate the gradient of a graph of the maximum static frictional force plotted against the normal force.
C	Calculate the $y$ -intercept of a graph of the maximum static frictional force plotted against the normal force.
D	Calculate the $y$ -intercept of a graph of the normal force plotted against the maximum static frictional force.

W	The material of the block is inversely proportional to the applied pulling force.
X	The mass of the system is inversely proportional to the tension in the string.
Y	The maximum static frictional force is directly proportional to the normal force.
Z	The tension in the string is directly proportional to the coefficient of maximum static friction.

A	the tension in the string
B	the magnitude of the pulling force
C	the coefficient of kinetic friction
D	the mass of the system

$M\,(\text{kg})$	$F_{\text{pull}}\,(\text{N})$
$\text{0,49}$	$\text{1,2}$
$\text{0,59}$	$\text{1,5}$
$\text{0,69}$	$\text{1,9}$
$\text{0,79}$	$\text{2,0}$
$\text{0,89}$	$\text{2,3}$

W	The coefficient of kinetic friction is inversely proportional to the tension in the string.
X	The mass of the system is inversely proportional to the applied pulling force.
Y	The kinetic frictional force is directly proportional to the coefficient of kinetic friction.
Z	The kinetic frictional force is directly proportional to the normal force.

Covering	Height $\text{(m)}$
paper	$\text{0,47}$
waxpaper	$\text{0,44}$
cellophane	$\text{0,24}$
sandpaper	$\text{0,66}$
tinfoil	$\text{0,38}$

A	Several different height readings for the same block covering should be taken.
B	The critical angle is higher for block coverings with higher coefficients of static friction.
C	It might be difficult to hold the plank steady when measuring the height.
D	Smoother surfaces have fewer irregularities in their surface that can interlock with each other. This reduces the electrostatic force of attraction between surface atoms which makes it is easier for surfaces to start sliding past each other.

A	Object A
B	Object B
C	Neither object
D	Impossible to tell

A	Crate A
B	Crate B
C	Neither crate
D	Impossible to tell

A	How you judge when the block starts to move needs to be done consistently.
B	Smoother surfaces have fewer irregularities in their surface that can interlock with each other. This reduces the electrostatic force of attraction between surface atoms which makes it is easier for surfaces to start sliding past each other.
C	The height at which the block starts to slide is higher for block coverings with higher coefficients of static friction.
D	The plank of wood used as the inclined plane might not be perfectly uniform.

A	Use the formula for maximum static friction $\begin{matrix} f_{s}^{max} = μ_{s} F_{N} \end{matrix}$ $\begin{array}{c} f_{\text{s}}^{\text{max}} = \mu_{\text{s}}F_{\text{N}} \end{array}$
B	Substitute the component of the gravitational force parallel to the slope at the critical angle $\begin{matrix} F_{g, ∥} = m g \sin (α_{c}) \end{matrix}$ $\begin{array}{c} F_{g,\parallel} = mg\sin({\alpha_{\text{c}}}) \end{array}$
C	Substitute the normal force at the critical angle $\begin{matrix} F_{N} = m g \cos (α_{c}) \end{matrix}$ $\begin{array}{c} F_{\text{N}} = mg\cos({\alpha_{\text{c}}}) \end{array}$ and add $mg\sin({\alpha_{\text{c}}})$ to both sides of the equation.
D	Divide both sides by $\cos({\alpha_{\text{c}}})$ and then use the trigonometric identity $\begin{matrix} \tan (α_{c}) = \frac{\sin (α_{c})}{\cos (α_{c})} \end{matrix}$ $\begin{array}{c} \tan(\alpha_{\text{c}}) = \dfrac{\sin({\alpha_{\text{c}}})}{\cos({\alpha_{\text{c}}})} \end{array}$
E	Divide both sides by $mg$ .
F	Use the definition of net force, $\vec{F}_\text{net}$ , as the vector sum of all forces parallel to the slope.
G	Use Newton's second law for an object in static equilibrium $\begin{matrix} {\vec{F}}_{net} = 0 \end{matrix}$ $\begin{array}{c} \vec{F}_\text{net} = 0 \end{array}$

A	$\vec{F}_{\text{up}}$	D	$\vec{F}_{\text{down}}$
B	$\vec{F}_{\perp,\text{up}}$	E	$\vec{F}_{\perp,\text{down}}$
C	$\vec{F}_{\parallel,\text{left}}$	F	$\vec{F}_{\parallel,\text{right}}$

A	acceleration and Newton's second law.
B	gravity and Newton's universal law of gravitation.
C	resistance to change in motion and Newton's first law.
D	change in momentum and Newton's second law in terms of momentum.

A	resistance to change in motion and Newton's law of inertia.
B	gravity and Newton's universal law of gravitation.
C	momentum and Newton's second law in terms of momentum.
D	acceleration and Newton's second law.

A	The box keeps moving in the same direction, with the same speed.
B	The box experiences a zero net force.
C	The box keeps moving at a constant velocity.
D	The influence of gravity on the box is reduced.

A	Her velocity remains constant.
B	It follows from Newton's third law of motion.
C	The floor of the bus exerts a net force on her.
D	Her inertia is conserved.

A	Kinetic energy is always conserved.
B	It follows from Newton's first law of motion.
C	The floor of the bus exerts a net force on her.
D	Her inertia is conserved.

A	of Newton's third law of motion.
B	he experiences a zero net force.
C	of kinetic energy conservation.
D	the floor of the train exerts a net force on him.

A	of Newton's third law of motion.
B	of kinetic energy conservation.
C	of Newton's first law of motion.
D	of conservation of inertia.

Newton's laws

1. Introduction

2. Force

3. Basic types of forces

3. Newton's laws

4. Frictional forces

5. Force and free-body diagrams

6. Components and resultants of forces

7. Newton's first law

8. Newton's second law

A	$m = \dfrac{F_{\text{net}}}{a}$
B	$m = a F_{\text{net}}$
C	$m = \dfrac{a}{F_{\text{net}}}$

A	$m = \dfrac{a}{F_{\text{net}}}$
B	$m = F_{\text{net}} a$
C	$m = \dfrac{F_{\text{net}}}{a}$

A	directly proportional to
B	independent of
C	inversely proportional to
D	always equal to

A	inversely proportional to
B	always less than
C	directly proportional to
D	independent of

A	$4F_{\text{net}}$
B	$\dfrac{1}{16}F_{\text{net}}$
C	$F_{\text{net}}$
D	$\dfrac{1}{4}F_{\text{net}}$

	Direction of motion	Direction of acceleration
A	down	down
B	up	down
C	up	up
D	down	up

A	The system moves up and down around an equilibrium point.
B	The acceleration and velocity of the system are both zero.
C	The system is stationary because it experiences the static frictional force.
D	The Newton's third law action-reaction pairs all cancel each other out.

A	The forces acting on the system are balanced and the system is stationary.
B	The system is stationary because it experiences the static frictional force.
C	The top block and the bottom block must have the same mass in order to be balanced.
D	The system gently swings from side to side.

A	$F_{\text{g}} - F$
B	$F_{\text{g}} - F\sin(\theta)$
C	$F_{\text{g}} + F\sin(\theta)$
D	$F_{\text{g}} + F$
E	$F_{\text{g}}$

A	$F_{\text{N}} = F_{\text{g}}$
B	$F_{\text{N}} > F_{\text{g}}$
C	$F_{\text{N}} < F_{\text{g}}$
D	Impossible to determine.